Calcule la medida de los ángulos faltantes “x” “y” “z” en los triángulos propuestos
Respuestas
Respuesta:
\begin{aligned}\text{Lado A}&=35\\[1em]\text{Lado B}&=70\\[1em]&\downarrow\\[1em]\text{Hipotenusa}&=\sqrt{A^2+B^2}\\[1em]&=\sqrt{35^2+70^2}\\[1em]&=\sqrt{1,225+4,900}\\[1em]&=\sqrt{6,125}\\[1em]&=\bold{78.26}\\[2em]\text{Angulo A}&=\frac{180\times\arcsin{\left(\frac{B}{\text{Hipotenusa}}\right)}}{\pi}\\[1em]&=\frac{180\times\arcsin{\left(\frac{70}{78.26}\right)}}{\pi}\\[1em]&=\frac{180\times\arcsin{\left(0.89\right)}}{\pi}\\[1em]&=\frac{180\times1.11}{\pi}\\[1em]&=\frac{199.3}{\pi}\\[1em]&=\bold{63.43}\\[2em]\text{Angulo B}&=\frac{180\times\arcsin{\left(\frac{A}{\text{Hipotenusa}}\right)}}{\pi}\\[1em]&=\frac{180\times\arcsin{\left(\frac{35}{78.26}\right)}}{\pi}\\[1em]&=\frac{180\times\arcsin{\left(0.45\right)}}{\pi}\\[1em]&=\frac{180\times0.46}{\pi}\\[1em]&=\frac{83.46}{\pi}\\[1em]&=\bold{26.57}\\[2em]\text{Area}&=\frac{A\times{B}}{2}\\[1em]&=\frac{35\times70}{2}\\[1em]&=\frac{2,450}{2}\\[1em]&=\bold{1,225}\\[2em]\text{Perimetro}&=A+B+\text{Hipotenusa}\\[1em]&=35+70+78.26\\[1em]&=\bold{183.26}\end{aligned}
Lado A
Lado B
Hipotenusa
Angulo A
Angulo B
Area
Perimetro
=35
=70
↓
=√
A
2
+B
2
=√
35
2
+70
2
=√
1,225+4,900
=√
6,125
=78.26
=
π
180×arcsin(
Hipotenusa
B
)
=
π
180×arcsin(
78.26
70
)
=
π
180×arcsin(0.89)
=
π
180×1.11
=
π
199.3
=63.43
=
π
180×arcsin(
Hipotenusa
A
)
=
π
180×arcsin(
78.26
35
)
=
π
180×arcsin(0.45)
=
π
180×0.46
=
π
83.46
=26.57
=
2
A×B
=
2
35×70
=
2
2,450
=1,225
=A+B+Hipotenusa
=35+70+78.26
=183.26